The coating of nanostructured features with homogeneous films or particles is a technological need in application fields ranging from semiconductor manufacturing to nanostructured photovoltaics, energy storage and catalysis. This problem has been studied previously in the context of different thin-film deposition techniques, including physical vapor deposition, chemical vapor deposition (CVD) (both thermal and plasma enhanced) and, more recently, atomic layer deposition (ALD).
In order to develop new processes and materials with the desired properties or to design better equipment is to understand how the experimental variables affect the coating process. To achieve this, computational models of varying degrees of complexity have been applied to the simulation of the coating process, and they are part of the prior art. In their more complete version, these models consider the transport and reaction of gases in a reactor, reacting cell or in general in a region of the space. In the most general processes, different species in the liquid or gaseous phase react with each other both in the same phase, on the surface of the material or inside the material itself. The growing material generally and/or its surface is also an active component of the overall reaction process.
A similar approach, but with potentially different models, can be applied to simulate the reaction and transport of gaseous or liquid species in nanostructured materials.
In one implementation, nanostructured materials are materials whose features are characterized by a size which is at least three orders of magnitude smaller than that of the reactor-scale simulation size in at least one dimension. These may include surfaces with microscopic features, porous particles, sculptural films, colloidal films or films composed of nanoparticles, nanotubes, fiber bundles, polymer and block-copolymer films, and textiles or surfaces with microelectromechanical devices or MEMS. The key aspect of these materials is that, due to the significant difference in length scale between reactor scale and the feature scale, a single model comprising both reactor and feature scale would be computationally very expensive, since it would force the reactor to be simulated with a degree of detail far exceeding that required to capture the phenomenology of the reactive transport outside the nanostructured substrate.
For these cases, the prior art has approached this problem by applying multiscale model approaches to the simulation of these systems: the reactor-scale model is solved at a length scale relevant for that problem, and a separate model takes place of the transport inside the nanostructured material, and those two models are linked in such a way that only the relevant information is passed between the two models to be able to solve the transport and reaction of species at both separate length scales simultaneously.
The state of the art approach to solve this problem can be summarized as folios: at a reactor scale, the simulation domain is divided in a series of interconnected regions. At any given iteration of the process, for every region facing the nanostructure substrate, the specific model for the nanostructure substrate is then applied and the transport inside the nanostructured material is solved. This means that, if it takes Nt iterations to solve the model to its completion (either because it converges to a stable solution or because, in a time-dependent simulation it reaches to the target final time) and there are Ns regions facing the nanostructured material, the nanostructured material model needs to be solved Nt×Ns times. This means that if the time Dt is very high, the repetitive application of the feature scale model becomes extremely time consuming part of the solution process.
One important feature of the prior art is that the state of the nanostructured material is constantly stored and updated in each iteration. For instance, the reactive transport in the nanostructured material can solved by applying a discretization algorithm to the nanostructured material in a similar way as described above for the reactor scale. The state of the system therefore is determined by the value of the relevant variables on each of the N discretized regions of the nanostructure. The state must be stored and updated for each of the Ns elements interfacing the nanostructured material at the reactor scale.
Consequently, the application of multiscale models to the simulation of the coating of nanostructured materials requires substantially more computational power and memory that the simulation on the flat surfaces. It also relies on two models that are intimately linked within the simulation, meaning that models that can solve the reactor scale transport in absence of nanostructured materials cannot be updated to incorporate the nanostructured materials without substantial rework. This makes it almost impossible to apply an existing reactor-scale model for the case of closed-source software.
The application domain of the current invention pertains to the synthesis of materials as thin films using a plurality of methods, including sputtering, evaporation, chemical vapor deposition, and atomic layer deposition. Of these methods, Atomic Layer Deposition is of particular relevance due to its time-dependent nature, which makes the application of simulations to model the growth process much more computationally expensive. Due to its self-limited surface chemistry, ALD is intrinsically conformal and therefore it can achieve uniform coatings in high aspect ratio features and large-area substrates. This attribute makes ALD intrinsically scalable, facilitating the transition from lab-scale research to prototype. However, beyond the prototype scale, the economic aspects of a process, such as throughput and materials utilization, become crucial for advancing the process to manufacturing. Moreover, small departures from ideal self-limited ALD surface chemistry, which may be irrelevant at a small length scales, can greatly condition the process at large scale. Therefore, advances in the way models are applied to the simulation of Atomic Layer Deposition can facilitate the scale up process and the design of more efficient tools, and impact fields as diverse as semiconductor processing, energy storage, solar energy, and catalysis.
From a theoretical perspective, one important advantage of ALD compared with CVD and plasma enhanced CVD (PECVD) is the lack of homogeneous processes: This greatly simplifies the task of developing general models applicable to a wide range of systems, especially when simple surface kinetic models are good approximations for the self-limited surface kinetics. For instance, in a previous work, the following expression was derived to predict the exposure required to coat a nanostructured feature under the common first-order irreversible Langmuir kinetics:
                              p          ⁢                                          ⁢                      t            c                          =                                                            2                ⁢                π                ⁢                                                                  ⁢                mkT                                                    s              0                                ⁢                      3            2                    ⁢                                    (              AR              )                        2                    ⁢                      (                          1              -                                                2                  ⁢                                      log                    ⁡                                          (                                              1                        -                                                  c                          0                                                                    )                                                                                        3                  ⁢                                                            β                      ⁡                                              (                        AR                        )                                                              2                                                                        )                                              1        )            
where AR is the aspect ratio of the feature; β is the bare reaction probability of the first-order irreversible Langmuir kinetic model for the ALD chemistry; s0 is the average area of a surface site; m is the precursor mass; k is the Boltzmann constant; p is the precursor vapor pressure; tc is the exposure time; c0 is the normalized coverage; and T is the temperature. While similar expressions can be obtained for the single-source precursor low-pressure CVD, these conditions represent only a small subset of the parameter space for CVD. In contrast, Eq. 1 applies to any ALD process that can be represented by this simple, ideal surface kinetics.
However, the simple first-order Langmuir kinetics that can be represented by Eq. 1 are sometimes insufficient to capture the complexities of the real-world ALD surface chemistry necessary for useful applications. Well-known instances include non self-limited surface recombination of species in radical and plasma enhanced ALD, ozone recombination, “parasitic” CVD, re-adsorption of gaseous products, and etching. Even the prototypical example for Al2O3ALD using trimethyl aluminum and H2O shows non-ideal behavior for the H2O saturation. In fact, it is safe to say that virtually all ALD processes are non-ideal in the limit of very large precursor exposures. Therefore, while the use of first-order kinetics (and with them Eq. 1) is useful to understand the universality of growth under ideal self-limited conditions, it fails to reproduce the nuances of some technologically relevant ALD processes. This problem is further amplified in the presence of nanostructured materials.
Thus, there is a need for systems and method to model real-world deposition processes on nanostructured materials that can accommodate complex precursor-surface interactions and that can be solved fast enough to allow their application to the optimization of a process, a reactor design, and the final product.